A Study of Replicators and Hypercycles by Hofstadter's Typogenetics

Abstract

A Typogenetics is a formal system designed to study origins of life from a “primordial soup” of DNA molecules, enzymes and other building materials. It was introduced by Hofstadter (1979) in his seminal book Dialogues with Gödel, Escher, Bach: An Eternal Golden Braid. Autoreplicating molecules and systems of mutually replicating and catalyzing molecules (autoreplicators and hypercycles) are modeled in the present paper in a form composed of two strands of symbols. These strands are vehicle of two fold information: The first one corresponds to information that is transferred by strands. The second type of information specifies a process of strand replication. The used replicating molecules - strands are created by an approach closely related to evolutionary algorithms. While a small hypercycle of two molecules mutually supporting their reproduction can be created without extreme difficulties, it is nearly impossible to create a hypercycle involving more than 4 autoreplicators at once. This paper demonstrates that larger hypercycles can be created by an optimization and inclusion of new molecules into a smaller hypercycle. Such a sequential construction of hypercycles can substantially reduce the combinatorial complexity in comparison with a simultaneous optimization of single components of a large hypercycle.